On Easter Sunday 1996 Tricky left his flat on Kensington High Street to buy his usual weed-smoking insomniac's breakfast of Lucozade and chocolate. When he reached the newsagent he had a sudden change of heart. "On the railings there's a big fucking poster of me as Jesus for Time Out magazine," he says, imitating a cartoonish double take. "On Easter day! I just went straight back into my house. It was surreal."

It's easy to forget just how famous and anomalous this cross-dressing west country Mephistopheles was during that Britpop-happy era. His debut album, 1995's Maxinquaye, was the anti-Parklife: a ghost world of dissolving identity, sexual turmoil, oblique violence and very dark jokes. It was, despite its creators' best efforts to the contrary, a hit. Tricky beat Blur, Oasis, Pulp and Elastica to album-of-the-year laurels in the music weeklies, was profiled for a magnificently pretentious magazine feature by none other than David Bowie and even, during a brief liaison with Björk, became paparazzi fodder. "I thought I'd be an underground artist," he says. "I had no idea it was going to do that and I was not ready for it."

Success, in Tricky's mind, ruined Maxinquaye, turning it into "a coffee-table album". Its increasingly hostile successors were designed to "kill all that Maxinquaye bullshit" and restore him to the cult status he had originally anticipated. It's still not his favourite record but when somebody suggested he reunite with his cryptic vocal foil Martina Topley-Bird to perform the album live he thought: why not? Although they parted ways creatively in 1998 (Topley-Bird has made three solo albums and worked with Massive Attack and Gorillaz), they've been in regular contact because of their daughter, Mazy, who is only one month younger than Maxinquaye. "It's like revisiting an old world," says Topley-Bird, who is droll and spacey where Tricky is hyperactively chatty. "I'm really intrigued."

They met on a Bristol street in 1991 when Tricky was still in Massive Attack and Topley-Bird, seven years younger, was revising for her GCSEs. Their backgrounds were as different as could be: her dad was celebrated direct marketing pioneer Drayton Bird; Tricky's disappeared before he was born and his mum, after whom Maxinquaye was named, killed herself when he was four. But shortly afterwards they met up again and recorded the hollowed-out hip-hop blues of Aftermath. He took it to Massive Attack for inclusion on Blue Lines but they weren't interested. She went to sixth-form college, with plans to study oceanography at university. Aftermath languished unheard for two years until Tricky's cousin suggested he try to get a record deal. To his surprise he quickly got one with Island, which meant he had to make an album.

What did he know about that? "Nothing," he says proudly. "Being naive I think is how you construct new music. When you start thinking too much what is it you're doing? You're just making an album. You're not doing brain surgery. If you take it too seriously you start taking yourself too seriously." What did he want to achieve? "To do an album that's going to fuck everybody up. No compromise whatsoever. Being a rapper back then was about not being seen, being undercover – fucking punk, y'know?"

In a 2007 interview about Maxinquaye, engineer and co-producer Mark Saunders said: "It was the most bizarre record I've ever worked on … Think of how to make a record, then forget everything you've learned and start completely backwards and upside down." Tricky didn't know how to craft songs or work the equipment but he knew what he wanted, even if it didn't make sense to anyone else. "I can remember arguing for two days with Mark Saunders about Strugglin'," he says. "He said: 'This can't work. It's not musically correct.' And I said: 'If I can hear it in my brain you can't tell me it can't work.'" Even Topley-Bird had her doubts. "There were definitely periods when I was feeling more hormonal and teenage and I'd get worried and think, God, this is really strange, how are people going to react?"

Topley-Bird appears on Maxinquaye more often than Tricky does. He wanted a prominent female vocalist because "it's my mum speaking through me; a lot of my lyrics are written from a woman's point of view," but he also used her to achieve stark gender dissonance, for example when she sings "I'm a black man" on a thrillingly counterintuitive rock version of Public Enemy's Black Steel in the Hour of Chaos. Almost every vocal was recorded in a single take, with Martina improvising melodies to words she had only just been given. "It was totally instinctive," she says. "There was no time to drum up an alter ego. I liked the idea that the information people needed about me was what they would hear when they put the record on. Anything else was sort of extraneous. I didn't think there was anything in my biography that would explain my musical choices."

When Maxinquaye was promptly declared a masterpiece, Topley-Bird, a 19-year-old new mother, kept her head down. "No one was more shocked than me, I have to tell you. I grew up with grunge bands complaining about being famous so I was suspicious of people. The rate of change was intense. I was definitely thinking, God, I should just run off to Italy or something. But it's cool that I did something like that when I was a teenager. I think it's quite sweet."

Tricky, who had nowhere to hide, admits he had problems acclimatising to attention, repeatedly clashing with journalists, record executives and audiences. "I had candida for years and it made me a not nice person so I fucked up a lot of relationships through being successful and being sick," he says ruefully. "I wish I didn't fuck up certain things but it ain't worth looking back. Now I have to remind myself if I get a bit of ego that it ain't about me. When you do it long enough you realise how lucky you are."

They both say this reunion will be temporary. Tricky has another album on the go and has just been in the studio with Massive Attack's 3D for the first time since the 90s. Last summer's Glastonbury festival triggered a deliciously odd flashback to his brief, anomalous spell as a pop star when he popped up as a surprise guest during Beyoncé's headlining set.

What does he think spectators made of him? "They just thought I was some nutter," he cackles. "I would have. I'd want to know who the fuck is this guy? It's strange enough to be interesting. It's kind of perverse."

• Tricky and Martina Topley-Bird perform Maxinquaye at O2 Academy Bristol on 26 April, IndigO2 in London on 27 April, and Manchester University on 28 April.